Designing a screened enclosure for use in close proximity to intense SHF radiation requires very careful consideration.
As suggested, the mesh over a microwave door does indeed screen the user against excessive uW radiation, but the mesh is flat and the user is not constantly in adjacent proximity to the door (square law of field strength and distance being what it is), all of which are factors considered in a "safe" microwave cooker design. The downside of a camera inside a screened enclosure, sitting inside a microwave oven, is a considerably more challenging environment - particularly for sensitive electronics which at-least should not be adversely affected if the intended application is to have merit at-all.
To begin, the screened enclosure should offer minimal electrical surface resistance, suggesting a coating of silver, nickel, or similar material with low resistivity due to the skin effect at high-frequency. A material of significantly higher electrical resistance
can increase the propensity for re-radiant "hot-spots" to develop - particularly around screws or fixings.
The box should have rounded corners to minimise the propensity for fundamental or harmonic resonance created by travelling waves across its surfaces (this would suggest a sphere as the most effective form of screened enclosure).
The thickness of the material has a bearing on screening effectiveness, as although travelling waves at high frequencies are constrained to the material surface, there is nevertheless an EM coupling to re-radiant inner surfaces of the box. Notably, Mu-metal is finding modern application for screened enclosures, as it has the effect of screening (effectively "repelling") magnetic fields - even
static magnetic fields. Externally coat an enclosure made of MuMetal, with a sprayed metal film offering low surface resistance, and you should have a pretty good screened enclosure on your hands

An aperture offering electrical screening whilst minimising interference to light can often be supplemented by ITO (Indinium Tin Oxide) coated glass, though sadly the effects are best observed in the tens of MH'z region. It's effects are
reflective (rather than conductive), offering typical figures of around 50-to-60dB attenuation at HF to only around 10-20dB at 1GHz, so hardly a worthwhile proposition for this application.
For the geeks, here's a pretty good online start for screened enclosure calculations (rarely accurate but a good
relative indicator as a starting point)...
http://www.emc.york.ac.uk/examples/screening/screening.htmlIf it were me, I would try experimenting with a small, inexpensive camera - removing the conventional lens and placing the bare CCD (with battery and and accompanying circuitry) inside a small screened ball or "curvy" enclosure - maximising screening efficiency by employing "pin-hole" focus on an externally-chamfered hole. You'd need plenty of light inside the uWave oven, but no need to mess around with camera focus... The optimum subject distance (capture area) would simply be the same as the size of the CCD surface and its distance from the pin-hole inside the screened enclosure, but will always remain in-focus with only a tiny pin-hole to optimise screening efficiency
Just a whacky early-morning thought
All the best,
FJ